相关论文: On some properties of Hopf manifolds

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

We investigate slice-quaternionic Hopf surfaces. In particular, we construct new structures of slice-quaternionic manifold on $\mathbb{S}^1\times\mathbb{S}^7$, we study their group of automorphisms and their deformations.

We give an account of old and new results concerning many types of non-K\"ahler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behaviour at deformations and blow-up. We also describe a…

We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry.

We propose a new method to investigate the dimension of the space of integrals on a Hopf algebra $H$ and other properties of $H$-comodules.

In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.

With the help of a new type of functionals we study manifolds diffeomorphic to $S^2\times S^2$ and establish, in particular, the Hopf conjecture.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

We study some topological properties of attractors.

We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.

A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…

In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.

Some geometric structures with associated Riemannian metrics have been considered in the book.

Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.

We investigate the structures of Hopf $\ast$-algebra on the Radford algebras over $\mathbb {C}$. All the $*$-structures on $H$ are explicitly given. Moreover, these Hopf $*$-algebra structures are classified up to equivalence.